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All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Dynamic polarizabilities of two-electron atoms, with rigorous upper and lower bounds

Methods are described for calculating rigorous upper and lower bounds to dynamic dipole polarizabilities for frequencies up to and beyond the first excitation threshold, even when (as usual) the field-free problem cannot be solved exactly. These methods were employed to calculate rigorous bounds to the dynamic polarizabilities of the two-electron atoms H(-), He, and Li(+), using well correlated trial wavefunctions up to 135 terms in length. The majority of previous theoretical and experimental results for these atoms can thereby be ruled out, including the highly precise Starkschall-Gordon values, which had heretofore appeared to be the most accurate available.

Glover, R. M.↗
NASA NTRS1977

Dynamic polarizabilities of metastable 2/1,3S/ excited states of He and Li/+/, with rigorous upper and lower bounds

Methods previously described for calculating rigorous upper and lower bounds to dynamic dipole polarizabilities are applied to the metastable 2(1S) and 2(2S) excited states of He and Li(+), using highly correlated variational trial functions. For each of these species, the bounds rigorously establish the values of the frequency-dependent dipole polarizability to within about 1% and appear to represent the first determination of this property at frequencies above the first excitation threshold.

Glover, R. M.↗
DOE OSTI2025

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗
NASA NTRS1965

Lower Bounds to Energy Eigenvalues for the Stark Effect in a Rigid Rotator

Upper and lower bounds have been calculated for the energy levels of a rigid rotator in an electric field, in order to study the problems associated with the use of the partitioning method for bracketing an eigenvalue of the Schrödinger equation. Results of arbitrarily high accuracy are possible in this example.

Choi, Jong H.↗
NASA NTRS1991

Analysis of upper and lower bounds of the frame noise in linear detector arrays

This paper estimates the upper and lower bounds of the frame noise of a linear detector array that uses a one-dimensional scan pattern. Using chi-square distribution, it is analytically shown why it is necessary to use the average of the variances and not the average of the standard deviations to estimate these bounds. Also, a criteria for determining whether any excessively noisy lines exist among the detectors is derived from these bounds. Using a Gaussian standard random variable generator, these bounds are demonstrated to be accurate within the specified confidence interval. A silicon detector array is then used for actual dark current measurements. The criterion developed for determination of noisy detectors is checked on the experimentally obtained data.

Jaggi, S.↗